Modal frequencies evaluation of a damaged bridge using RCVMD algorithm based on sensor dynamic responses

Abstract This paper aims to employ high-rate global navigation satellite system real-time kinematic (GNSS-RTK) and triaxial accelerometer sensors to evaluate the modal frequencies of a damaged long-span bridge based on the proposed modified variational mode decomposition algorithm. Firstly, in the modified VMD, the relative root mean square error was presented to optimize the decomposition parameter K , the correlation criterion was introduced to select the suitable intrinsic mode function components. The above procedure is called the RCVMD algorithm. Subsequently, the performance comparison evaluation experiments proved that the RCVMD algorithm was more advantageous in the decomposition and reconstruction of signals, had a better noise reduction effect in the signal with different noise levels, and was suitable to process the actual measurement response. Finally, in the field experiment, the modal frequencies of the damaged bridge were correctly detected from the GNSS-RTK displacement and acceleration responses according to the RCVMD algorithm, and the accelerometer picked up the high-order structural frequencies, demonstrating the reliability of the proposed method. The frequency characteristics of the damaged bridge are different from the normal state. The first and third-order frequencies increase, which is especially obvious in the first-order frequency, yet the second-order frequency decreases. The measured results have practical applications and can provide data support for the maintenance of the damaged bridge.